Sharaf al-Dīn al-Ṭūsī on the number of positive roots of cubic equations (Q1119549)

The paper comments on the Algebra of Sharaf al-Dīn al- Ṭūsī as explained by R. Rashed. Al-Ṭūsī found out correctly all the positive roots of the Al-Khayyāms 13 forms of the equation. In his second volume of the edition Rashed explains the solution of the last five forms through methods of analytical geometry not known before the 17th century. The author gives another explanation built upon ancient and medieval lines of reasoning. The paper consists of 12 1/2 pages, about 3 of notes showing errors in the edition and a list of references.